Structural Concrete - Hassoun

Appendix B Design Tables (SI Units) 1009
Table B.4
Values of ρ max
,R u,max
, ρ b
, ρ min
ρ b =0.85β 1 (f ′ c ∕f y )[87∕(87 + f y )] ρ max =(0.003 + f y ∕E s )ρ b ∕0.008 R u = φρf y [1−ρf y ∕1.7f ′ c ]
f y
= 280 MPa
f y
= 350 MPa
f ′ c MPa 100 ρ max
R u,max
MPa 100 ρ b
100 ρ min
100 ρ max
R u,max
MPa 100 ρ b
100 ρ min
21 2.031 4.32 3.71 0.50 1.624 4.32 2.75 0.40
28 2.715 5.77 4.96 0.50 2.167 5.77 3.67 0.40
35 3.180 6.85 5.81 0.53 2.551 6.85 4.32 0.42
42 3.575 7.78 6.53 0.58 2.864 7.78 4.85 0.47
f y
= 420 MPa
f y
= 525 MPa
f ′ c MPa 100 ρ max
R u,max
MPa 100 ρ b
100 ρ min
100 ρ max
R u,max
MPa 100 ρ b
100 ρ min
21 1.356 4.32 2.14 0.33 1.082 4.32 1.55 0.27
28 1.806 5.77 2.85 0.33 1.445 5.77 2.07 0.27
35 2.123 6.85 3.35 0.35 1.704 6.85 2.44 0.28
42 2.389 7.78 3.77 0.39 1.920 7.78 2.75 0.31
Note: ρ max
values are for ε t
= 0.005 and φ = 0.9.
Table B.5
Suggested Design Steel Ratios, ρ s
, and Comparison with Other Steel Ratios
f ′ c
f y
100 100 100 R u
for Ratio Ratio Weight of ρ s
MPa MPa ρ b
ρ max
ρ s
ρ s
(MPa) ρ s
/ρ b
ρ s
/ρ max
(kg/m 3 of concrete)
21 280 3.71 2.04 1.4 3.16 0.377 0.689 112
350 2.75 1.63 1.2 3.35 0.436 0.739 96
420 2.15 1.37 1.2 3.91 0.558 0.885 96
28 280 4.96 2.73 1.4 3.25 0.282 0.516 112
350 3.67 2.18 1.4 3.97 0.381 0.646 112
420 2.85 1.81 1.4 4.65 0.491 0.775 112
35 280 5.81 3.20 1.6 3.72 0.275 0.503 128
350 4.32 2.57 1.6 4.58 0.370 0.627 128
420 3.35 2.16 1.6 5.39 0.478 0.754 128
Note: ρ max
values are for ε t
= 0.005 and φ = 0.9.
Table B.6
Minimum Thickness of Beams and One-Way Slabs
Yield
Strength Simply One End Both Ends
Member f y
(MPa) Supported Continuous Continuous Cantilever
Solid one-way slabs 280 L/25 L/30 L/35 L/12.5
350 L/22 L/27 L/31 L/11
420 L/20 L/24 L/28 L/10
Beams or ribbed one-way slabs 280 L/20 L/23 L/26 L/10
350 L/18 L/20.5 L/23.5 L/9
420 L/16 L/18.5 L/21 L/8